IMPROVED COST OF ENERGY COMPARISON OF
PERMANENT MAGNET GENERATORS FOR LARGE
OFFSHORE WIND TURBINES
Kerri Hart
University of Strathclyde
kerri.hart@strath.ac.uk
Alasdair McDonald
University of Strathclyde
alasdair.mcdonald@strath.ac.uk
Edward Corr
University of Strathclyde
edward.corr@strath.ac.uk
Abstract:
This paper investigates geared and direct-drive
permanent magnet generators for a typical
offshore wind turbine, providing a detailed
comparison of various wind turbine drivetrain
configurations in order to minimise the Cost of
Energy. The permanent magnet generator
topologies considered include a direct-drive
machine and single stage, two-stage or threestage gearbox driven generators. The cost of
energy calculations are based on initial capital
costs, the costs of manufacture, installation,
operations and maintenance, with particular focus
on improved calculations of the annual energy
yield with better availability estimations and
gearbox loss modelling.
Keywords: Cost of energy, permanent magnet
generator, direct-drive, gearbox, wind turbine.
1
Introduction
This paper builds on the work of Polinder et al. [1]
and Bywaters et al. [2] but with an emphasis on a
typical 6MW offshore wind turbine. This paper
considers the four following generator topologies:
the direct-drive permanent magnet generator
(DDPMG), the permanent magnet generator with
single stage gearbox (PMG1G), the permanent
magnet generator with two-stage gearbox
(PMG2G), and the permanent magnet generator
with three-stage gearbox (PMG3G).
Offshore wind farm development has rapidly
increased in the past few years. The issues and
limitations present in onshore wind farm
development, such as turbine size and noise
production, are much less prevalent offshore, and
combined with excellent wind resources offshore
wind farms are becoming more attractive to
developers on a global scale. However, the harsh
sea environment poses several issues for
Henk Polinder
Delft University of Technology
h.polinder@tudelft.nl
James Carroll
University of Strathclyde
j.carroll@strath.ac.uk
developers
such
as
installation
and
scheduled/unscheduled maintenance. Weather
windows can be unpredictable and often too short
to carry out significant repairs and so developing
reliable and efficient wind turbines is of extreme
importance. Large wind turbines (>5 MW) are now
being manufactured to allow a fewer number of
turbines to be installed in an offshore site whilst
maintaining high energy yield. By reducing the
number of installed turbines the service and repair
requirements can be minimized.
Over the past few decades, wind turbine
manufacturers have been exploring various drive
train topologies ranging from multistage gearbox
and induction generators to gearless direct-drive
systems. With high emphasis on turbine reliability
for modern offshore developments, some
manufacturers are beginning to concentrate on
using direct-drive generators which do not have a
gearbox (eliminating gearbox related failures).
Direct-drive technology might offer reduced
maintenance cost and complexity and improved
reliability [3]. However, these slow speed
generators need to be large, able to deliver high
torque and robust enough to cope with large forces
that might be avoided by using a gearbox.
Therefore, direct-drive machines tend to be large,
heavy and are expensive.
With an aim to further enhance performance and
reliability, manufacturers are also implementing
permanent magnet (PM) systems into their
turbines to eliminate excitation losses. Permanent
magnet machines do not require additional power
supply for the magnet field excitation and have
higher efficiency and reliability [3] compared with
electrically excited machines. Sizing and cost
become significant issues with direct-drive PM
configurations as generators may require very
large diameters and so can be heavy and
expensive which in turn can create transport and
installation issues. As a result, turbine
manufacturers have also been considering hybrid
systems consisting of a permanent magnet
generator and single-stage or 2-stage gearboxes.
The gearbox and generator can either be separate
or integrated together, for example the Multibrid
systems – such as the AREVA M5000. Both
approaches represent a compromise between high
speed geared systems and direct-drive systems.
Medium speed solutions require a smaller
generator than a direct-drive generator.
In this paper the authors limit analysis and
discussion to drivetrains with permanent magnet
generators – which are currently the preferred
solution for a majority of manufacturers of offshore
wind turbines. The generator systems considered
in this paper are as follows:




DDPMG – Direct-drive
generator
PMG1G – Permanent
single-stage gearbox
PMG2G – Permanent
two-stage gearbox
PMG3G – Permanent
three-stage gearbox
permanent magnet
2
Modelling Methodology
The design of the wind turbine and the generator
configurations are based on approximations and
values found in Polinder’s paper [1]. The generator
dimensions of the 3 MW wind turbine that form the
basis of that study are scaled by the generator
torque to maintain consistent comparisons for the
6 MW turbine considered in this paper. The geared
generator concepts have their gear ratio design
based on current manufacturers design and some
limited optimisation. The costs of the generator
configurations are based on the mass of materials
used in each generator and material cost in Table
1. Other costs such as construction and the costs
of the converter are scaled with an inflation rate of
2.4% p.a. [4] to be in accordance with the present
day value.
magnet generator,
magnet generator,
magnet generator,
Whilst being cognisant of promising alternatives to
the gearboxes (hydraulic and electromechanical
gearboxes) and PM generators (DFIGs, brushless
DFIGs and HTS generators), the authors want to
address the question ―which PM generator
drivetrain delivers the lowest cost of energy
offshore?‖ The variation in turbine designs
suggests that different manufacturers have come
to different conclusions.
The contribution of this paper is that it compares
different permanent magnet generators on a cost
of energy basis. The paper begins with a section
on the modelling of the wind turbine, gearbox,
converter and the generator. The details of the four
different generator topologies are then described
and their simulated performances are analysed
which includes a sensitivity analysis. The paper
concludes with a comparison of the four generator
concepts and which configuration may offer the
most economic cost of energy.
Wind Turbine Characteristics
Rated Grid Power (MW)
Rotor Diameter (m)
Rated Wind Speed (m/s)
Rated Speed (rpm)
Optimum Tip Speed Ratio
Maximum Aerodynamic Efficiency (%)
Mass density of air (kg/m3)
6
140
11
12
8
48
1.225
Generator Material Characteristics
Slot filling factor ksfil
Remnant flux density of magnets Brm (T)
Recoil permeability of the magnets μrm
Resistivity of copper at 120οC ρCu (μΩm)
Eddy-current losses in laminations at 1.5 T, 50 Hz
PFe0h (W/kg)
Hysterisis losses in laminations at 1.5 T and 50 Hz
PFe0h (W/kg)
0.6
1.2
1.06
0.025
0.5
2
Loss Modelling
Maximum losses in a 6 MW VSI Pconvm (kW)
180
Cost Modelling
Single-stage gearbox (ratio 8) cost (kEuro)
Two-stage gearbox (ratio 40) cost (kEuro)
Three-stage gearbox (ratio 100) cost (kEuro)
Power electronics cost (Euro/kW)
Laminations cost (Euro/kg)
Copper cost (Euro/kg)
Permanent magnet cost (Euro/kg)
Rest of wind turbine cost (Euro)
672
1170
1330
40
3
15
48
6100
Table 1: Modelling Characteristics.
A baseline scenario is presented with typical
drivetrain losses, costs and ratings. Using the
same designs, further scenarios are investigated.
In two scenarios the gearbox or the generator is
replaced once in its lifetime for each of the
drivetrains, and in another the cost of permanent
magnets increases. These represent credible risks
that drivetrain designers must consider.
2.1
Wind Turbine Model
The comparison of the four generator systems was
achieved through the simulation of a theoretical 6
MW wind turbine with a rated speed of 12 rpm.
The aerodynamic power of a wind turbine is given
by the following equation:
(1)
where
is the mass density of air, r is the rotor
radius of the wind turbine, vw is the wind speed,
and Cp is the power coefficient (or aerodynamic
efficiency) which is a function of tip speed ratio
and pitch angle . The Weibull distribution
that describes the variation in wind speed at a
given site over a year is given in equation (2)
below:
( )
[ ( ) ]
(2)
where k is the shape parameter, C is the scale
parameter, and v is the wind speed.
The annual energy production (AEP) is calculated
based on the Weibull probability distribution:
∫
(3)
where vi is the cut-in wind speed and vc is the cutout wind speed if the turbine.
6
4
2
0
Probability
Power (MW)
The power curve and Weibull distribution of the
turbine are shown in Figure 1. The cut-in wind
speed is 4 m/s and the cut-out wind speed is 25
m/s with a rated power of 6 MW being attained at a
wind speed of 11 m/s. The parameters for the
Weibull distribution are based on a location in the
North Sea with a mean wind speed of 9.8 m/s, a
scale parameter of 10.8 and a shape parameter of
2.32.
0
5 10 15 20 25
0.1
0.08
0.06
0.04
0.02
0
Wind Speed (m/s)
(5)
Cost functions for two-stage gearboxes are more
difficult to find. In this case we assume an average
of equations (4) and (5); this gives equation (6). In
this study the gear ratio is chosen to be 40.
(6)
In previous studies (e.g. [1], [6]) gearbox losses
have been approximated based on an assumption
that 1% of viscous losses per gearbox stage are
reasonable. Reference [1] used x = 3% for a 3stage gearbox and x=1.5% for a single-stage
gearbox and scaled the loss using a ratio of actual
rotational speed (n) to rated rotational speed
(nrated). Prated is the wind turbine power:
(7)
The losses in an example 3-stage gearbox
topology [7] were calculated according to equation
(7). These are shown by the ―Scaled 3% loss
model‖ curve in Figure 2 for a 2.5MW turbine. A
more sophisticated approach was then used to
calculate the losses. ISO/TR 14179-1:2001
standards [8] specify likely losses for cooling
requirements and where applied to the gear and
bearing data from [6]. The losses from this method
are given in Figure 2 by the ―ISO method‖ curve. It
shows that equation (7) can overestimate gearbox
losses over the whole wind speed range and
particularly at low-medium wind speeds.
0 5 10 15 20 25
Wind Speed (m/s)
Figure 1. Power curve and Weibull distribution
as a function of wind speed.
2.2
Gearbox Modelling
The cost of gearboxes is difficult to estimate given
the variety in topologies and manufacturers.
However Fingersh et al. give some useful
expressions as a starting point [5].
Figure 2. Comparison of gearbox loss models for a
2.5MW wind turbine
Reference [5] gives an estimate of the cost (in €)
of the single-stage gearbox following equation (4).
In this case we use a gear ratio of 8.
(4)
The ratio of the three-stage gearbox is chosen to
be 100 and an estimate of the cost of the gearbox
is given by [5]:
Figure 3: Gearbox efficiency curves used in
this study
The data from [6] was used to calculate losses
associated with the first, second and third stages
of the gearbox. These losses were then scaled to
the required gearbox sizes for this study. The
gearbox efficiency curves for the chosen designs
are presented in Figure 3.
2.3
The flux density directly above a magnet in the air
gap of a permanent magnet machine is calculated
as:
̂
(
)
(11)
where Brm is the remanent flux density of the
magnets (1.2T), bp is the magnet width and τp is
the pole pitch.
Converter Modelling
In this study all of the drivetrains require a fully
rated converter as permanent magnet generators
are used.
Back-to-back power converters can be used as the
interface between the turbine generator and the
grid by implementing PWM (pulse width
modulation) to ensure a steady sine-wave output
from the variable speed operation of the turbine.
The power converter consists of a series of IGBTs
that make up a generator side converter, a grid
side inverter, and a DC-link capacitor. The losses
in the power converter are modeled using the
following equation:
(
(8)
)
where
is the dissipation in the converter at
rated power (3% of the rated power of the
converter), Is is the generator side converter
current, Ism is the maximum generator side
converter current, Ig is the grid side inverter
current, Igm is the maximum grid side inverter
current [1].
The no-load voltage induced by the flux density in
a stator winding is given by:
̂
√
(12)
where ωm is the mechanical angular speed of the
rotor. The copper losses in the generator are
2
calculated from the currents and resistances (I R
losses). The specific iron losses are given by:
( )(
̂
̂
)
( ) (
̂
̂
(13)
)
where fe is the frequency of the field in the iron,
is the hysteresis loss per unit mass at the
given angular frequency f0 and flux density B0, and
is the eddy current loss per unit mass.
2.5
Cost of Energy
The cost of energy (COE) [2] per MWh is the
overall outcome of this study and is calculated
using the following equation:
(14)
2.4
Generator Modelling
Equivalent circuit models are used to compare the
generators are described in [1]. The magnetized
inductance of an AC machine is given by:
(9)
where ls is the stack length in axial direction, rs is
the stator radius, Ns is the number of turns of the
phase winding, kw is the winding factor, p is the
number of pole pairs, and geff is the effective air
gap. The effective air gap is given by:
(
)
(10)
where ksat is a factor representing the reluctance of
the iron in the magnetic circuit, kCs is the Carter
factor for the stator slots, g is the mechanical air
gap, µrm is the relative recoil permeability of the
magnets, and lm is the magnet length in the
direction of the magnetization.
where FCR is the Fixed Charge Rate, ICC is the
Initial Capital Cost of the turbine, AOM is the
Annual Operation and Maintenance and AEP is
the Annual Energy Production.
In this case ICC is made up of a fixed part which
represents the rest of the wind turbine (common to
all of the designs) and a part which equals the cost
of the generator, any gearbox and the power
converter.
AOM is calculated according to [5] which uses a
cost/MWh energy produced ratio for calculating
operation and maintenance costs. It ignores the
effect of drivetrain choice of maintenance cost –
unfortunately there is a lack of data that
distinguishes operation and maintenance costs of
different types of offshore wind turbine drivetrains.
AEP is calculated using the methods described in
Section 2 as well as availability data given in Table
2. These availability figures are based on failure
rates that are synthesised from various reliability
studies and onshore mean time to repair modified
to include extra downtime for offshore work and
delays. For more details the reader is referred to
the paper by Carroll [9].
3
Results
The results for all four designs are presented in
Table 2. The following sections details the loss
mechanisms and costs for each of the designs.
DD
PMG
PMG
PMG
1G
2G
Generator Specifications
Generator speed (rpm)
12
96
480
Gearbox ratio
1:8
1:40
Stator radius rs (m)
3.5
2.5
0.7
Stack length ls (m)
1.5
0.4
0.8
Number of pole pairs p
100
54
10
Air gap g (mm)
7
5
1.4
Stator slot width bss (mm)
17
21
19
Stator tooth width bst (mm)
20
27
23
Stator slot height hss (mm)
80
80
80
Stator yoke height hsy (mm)
40
40
40
Rotor yoke height hry (mm)
40
40
40
Magnet height lm (mm)
15
15
15
Magnet width bp (mm)
87.5
116
178
Generator Parameters
Main inductance Lm (mH)
8.3
1.9
3.7
Stator leakage inductance
Lsσ (mH)
10.4
1.3
0.9
Stator resistance Rs (mΩ)
181
32.5
20.9
Generator Material Weight (ton)
Iron
30.6
6.4
3.3
Copper
6.6
2.0
1.0
PM
2.9
0.6
0.3
Total
40.1
9.0
4.6
Cost (kEuro)
Generator active material
330
77
39
Generator construction
436
115
24
Gearbox
672
1170
Generator system cost
767
864
1240
Converter
283
283
283
Other wind turbine parts
6000
6000
6000
Total cost of wind turbine
7050
7250
7520
Annual Energy
Copper losses (MWh)
1120
201
135
Iron losses (MWh)
151
242
243
Converter losses (MWh)
880
861
868
Gearbox losses (MWh)
0
314
779
Availability (%)
93.4
93.0
92.8
Total losses (MWh)
2150
1620
2030
Energy yield (GWh)
28.0
28.6
28.3
Cost of Energy
ICC (kEuro)
21400
22000
22800
AOM (kEuro)
628
641
635
FCR
0.116
0.116
0.116
COE (Euro/MWh)
110.7
111.3
115.6
PMG
3G
1200
1:100
0.5
0.9
3
1
33
40
80
40
40
15
417
8.3
0.4
12.1
2.8
1.1
0.3
4.2
38
10
1330
1380
283
6000
7660
79
529
894
879
92.6
2380
28.2
23200
632
0.116
117.7
Table 2: Design details, costs and performance
of 4 drivetrains
3.1
Results from the MATLAB model for the DDPMG
are shown in Figure 4. The results shown include
voltage and current levels, the wind turbine power
curve, the system efficiency and losses. The
system efficiency takes into account bearing and
cable losses as well as generator and converter
losses. In this case the generator diameter was
restricted to 7m. The significant losses in the
system result from high copper losses that account
for over half of the total losses. This is due to the
requirement that in order to produce a high torque
there is a large number of coils. Availability is high:
even though there are increased winding failures
in the direct-drive generator, there is no downtime
due to a gearbox.
DDPMG
Overall this drivetrain gave the lowest Cost of
Energy in the baseline study. The Siemens SWT6.0 150 and Alstom Haliade turbines – although
very different machines – fit into this category.
Figure 4: DDPMG Drivetrain Operation &
Performance
3.2
PMG1G
This drivetrain a similar but slightly higher Cost of
Energy than the direct-drive machine. Although it
has a lower rating than the turbine discussed here,
the AREVA M5000 would be a good exemplar of
the single-stage PM generator drivetrain. Results
are shown in Figure 5 and Table 2.
Because of its smaller torque rating the electrical
machine is smaller and cheaper (in terms of
materials and construction) than the direct-drive
generator. The addition of the gearbox does make
it more expensive (than the direct drive machine)
from the view point of capital costs.
The real benefit of a PMG driven by a single-stage
gearbox is the low losses with copper losses, iron
losses and gearbox losses all being fairly
balanced.
Although there is a gearbox – which means that
there are failures and downtime over and above
the direct-drive machine – there are less electrical
failures because the generator is smaller. Offshore
availability is very similar to the direct-drive
machine.
However, due to having a two-stage gearbox, the
gearbox losses become more significant and the
gearbox itself is larger and more expensive.
3.4
3.3
PMG3G
Figure 5: PMG1G Drivetrain Operation &
Performance
The PMG driven by a 3-stage gearbox has not yet
been a popular choice in the offshore wind market,
although the leading generator manufacturers
such as ABB and the Switch have high speed
PMGs in the 5-7MW range. As one might expect,
the generator is very compact, cheap and efficient.
Unfortunately the increased losses, cost and
downtime due to the additional gearbox stage give
rise to a higher Cost of Energy than all of the other
drivetrains. Results from the MATLAB model for
the PMG with a 3-stage gearbox are shown in
Figure 7 and Table 2. It might be attractive should
the cost of permanent magnets become very high
or if owners believe that they will have to replace
many generators in their fleet.
Figure 6: PMG2G Drivetrain Operation &
Performance
Figure 7: PMG3G Drivetrain Operation &
Performance
PMG2G
The Gamesa G128-5.0 MW and Samsung S7.0171 turbines adopt a 2-stage gearbox with a
permanent magnet generator. Results are shown
in Figure 6 and Table 2.
Here the Cost of Energy is higher than the directdrive and PMG1G. Overall losses and costs are
higher than the drivetrains with slower generators;
availability is marginally worse because of the
added failures in the gearbox when a second
stage is added.
The generator size is considerably smaller than
the single-stage gearbox design and so has
reduced losses in the stator. This lightweight
generator would also be advantageous to
developers
during
installation
procedures.
4
Sensitivity Analysis
Once designed and in production, the Cost of
Energy of an offshore wind turbine is somewhat
dependent on future events such as material price
changes and sub-assembly failure rates. In this
section the model is used to look at the sensitivity
to some of these factors.
COE (Euro/MWh)
COE: 1 gearbox
replacement (Euro/MWh)
COE: 1 generator
replacement (Euro/MWh)
DD
PMG
PMG
1G
PMG
2G
PMG
3G
110.7
111.3
115.6
117.7
110.7
114.4
120.9
123.8
114.0
112.2
115.9
117.8
Table 3: Sensitivity analysis for different
scenarios
4.1
Gearbox and generator
replacement scenarios
There have been some wind farms where there
have been a significant number of gearbox
replacements required. What happens to the cost
of energy if there is one gearbox replacement per
turbine over the lifetime of the wind farm? This can
be modelled by modifying equation (14) and
adding a replacement cost for one gearbox
replacement or one generator replacement. Table
3 shows the change in cost of energy (from the
baseline study in section 3). The increase in Cost
of Energy for the geared drivetrains demonstrates
gives a clearer advantage for the direct-drive
machines.
On the other hand the geared drivetrains are less
sensitive to the cost of having to replace a
generator once in the wind turbine’s life. Under this
scenario it is the single-stage design which has the
lowest Cost of Energy.
4.2 Permanent magnet cost increase
scenario
The last scenario in this study looks at the
sensitivity of Cost of Energy to changes in
permanent magnet prices. Future changes in
magnet costs mainly affect a portion of the
generator part of the initial capital cost (ICC)
component in equation (14). The baseline cost of
the magnets is €48/kg; here the same baseline
designs but with a scenario of €120/kg are also
tested. Figure 8 shows these points. If all other
factors are constant then the Cost of Energy
changes linearly. The direct-drive design has the
highest gradient, reflecting the high magnet
content in lower speed, higher torque generators.
One can interpret Figure 8 as showing that a future
magnet cost change from €48/kg to €60/kg would
make the permanent magnet generator with a
single-stage gearbox more attractive than the
direct-drive option.
5
Discussion and Conclusions
This study provides a comparison between four
different drivetrain configurations using permanent
magnet generators. The drivetrains were modelled
to assess which drivetrain configuration offers the
lowest Cost of Energy solution for a large offshore
wind turbine.
A direct-drive option can deliver the lowest Cost of
Energy. This is shown in both the baseline study
and when a gearbox replacement is required (for
the other candidate designs). Permanent magnet
generators have a limited track record in the wind
industry (particularly offshore) and so the scenario
of a generator replacement – once during the
turbine’s lifetime – is not unreasonable. Here the
direct-drive generator is second best. Even under
significant permanent magnet cost increases (i.e.
×2.5) this drivetrain fairs well, though once the
magnet price increases above about €60/kg it is
inferior to the single-stage gearbox machine.
Some potential disadvantages of the direct-drive
generator have not been captured in this study:
any increased wind turbine costs if the tower,
foundation and installation costs increase because
if increased top head mass is large; also changes
in operation and maintenance costs which depend
on the drivetrain. The availability has been based
on onshore failure rate data in the absence of real
operating data of offshore wind turbines with
direct-drive PMGs.
In this study the diameter of the direct-drive
generator was limited to 7m – this was assumed to
be pragmatic in terms of transportation – and
based on an air-cooled design. The optimisation
consistently delivered designs at this limit which
suggests that a large diameter machine would
deliver an even lower Cost of Energy (by
producing higher efficiency with the same amount
of expensive active material). This is an
opportunity for offshore wind turbines where
transportation restrictions are not as strict as
onshore.
The PMG1G performs well in terms of both energy
yield and COE. The single stage gearbox concept
outperforms the other gearbox designs, reinforcing
the benefits of the ―Multibrid‖ design. In the
scenario with one gearbox replacement, there was
a slightly bigger difference between the COE for
the DDPMG and the PMG1G. For scenarios with a
generator replacement or when the magnet cost
increases by a reasonable amount this drivetrain
delivers the lowest Cost of Energy.
Figure 8: Sensitivity to change in permanent
magnet price.
This study did not define the amount of integration
of generator and gearbox; it is possible that some
Trans. Energy Convers., vol. 24, no. 1, pp.
82–92, Mar. 2009.
highly integrated designs might lead to higher
maintenance and replacement costs.
The higher speed generator drivetrains faired
much worse under the baseline and other
scenarios. Gearbox cost reductions below the
assumed values predicted by equations (5) and (6)
may help reduce Cost of Energy to more
competitive levels under the combined scenarios
of higher magnet costs and a generator
replacements.
Acknowledgments
[4]
Trading Economics, Euro Area Inflation
Rate.
[Online]
[Cited
20/7/12]
http://www.tradingeconomics.com/euroarea/inflation-cpi.
[5]
L. Fingersh, M. Hand, and A. Laxson,
―Wind turbine design cost and scaling
model,‖ no. December, 2006.
[6]
J. Cotrell, "A preliminary evaluation of a
multiple-generator drive train configuration
for wind turbines." In 21st American Society
of Mechanical Engineers (ASME) Wind
Energy Symposium, 2002.
[7]
S. Sheng and C. Broomfield, ―Wind Turbine
Gearbox Condition Monitoring Round
Robin Study – Vibration Analysis," NREL,
Golden, Colorado, Report no. NREL/TP5000-54530, 2012.
[8]
Anon, ―Gears — Thermal capacity —Rating
gear drives with thermal equilibrium at 95°C
sump temperature," ISO/TR 14179-1:2001,
2001.
[9]
J. Carroll, A. McDonald, ―Drivetrain
Availability in Offshore Wind Turbines,"
Abstract submitted to EWEA 2014,
Barcelona 2014.
This work has been funded by the EPSRC, project
reference number EP/G037728/1.
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